Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x - 6$ and $ BC = 7x - 10$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x - 6} = {7x - 10}$ Solve for $x$ $ -x = -4$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({4}) - 6$ $ BC = 7({4}) - 10$ $ AB = 24 - 6$ $ BC = 28 - 10$ $ AB = 18$ $ BC = 18$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {18} + {18}$ $ AC = 36$